Half-implicit difference scheme for numerical simulation of transient processes in semiconductor devices

Polsky, B.; Rimshans, Janis

doi:10.1016/0038-1101(86)90211-x

Cited by 15 publications

(2 citation statements)

References 13 publications

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“…where W k n is a normalization function and p 0 is a real number (similarly as in [24], it can be shown that W k n and p 0 should not affect the final coefficients of a difference scheme), a monotone, exponential difference scheme has been developed:…”

Section: Numerical Resultsmentioning

confidence: 99%

Polarization kinetics in ferroelectrics with regard to fluctuations

Kaupužs¹,

Rimshans²,

Smyth³

2008

Modelling Simul. Mater. Sci. Eng.

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Polarization in ferroelectrics, described by the Landau-Ginzburg Hamiltonian, is considered, based on a multi-dimensional Fokker-Planck equation. This formulation describes the time evolution of the probability distribution function over the polarization field configurations in the presence of a time dependent external field. The Fokker-Planck equation in a Fourier representation is obtained, which can then be solved numerically for a finite number of modes. Calculation results are presented for one and three modes. These results show the hysteresis of the mean polarization as well as that of the mean squared gradient of the polarization.

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Section: Numerical Resultsmentioning

confidence: 99%

Polarization kinetics in ferroelectrics with regard to fluctuations

Kaupužs¹,

Rimshans²,

Smyth³

2008

Modelling Simul. Mater. Sci. Eng.

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“…For the automatic time step selection, there is a little difference between our method and [39]. We utilized the relative difference 8* between the exact solution and the approximate solution of the carrier density at time level (t+1) to select a new time step.…”

Section: The Numerical Methods For the Transient Problemmentioning

confidence: 99%

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Cui¹

1997

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Public reporting burden for this collection of information * estimated to average 1 hour per response, including the time for reviewing «utructtoni, searching existing data sources, gathering and maintaining the data needed, and compleung and reviewing the collection of information. Send comment regarding «is burden estsnates or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations Hong-Liang Cui Department of Physics and Engineering PhysicsPerformance Period:October 1,1994 -September 30,1997Contract Number: DAAH04-94-G-0413 a 2 December 1997 IntroductionIt is becoming increasingly important to use computer-aided device simulators in the design and fabrication processes of semiconductor devices designing as semiconductor devices continue to decrease in size toward the deep submicron regime. The development of devices involves several iterations of trial and error in fabrication until a specified goal in terms of design conditions is reached. The application of device modeling can provide an inexpensive way to analyze and design the semiconductor devices before expensive device processing. Since traditional equivalent circuit models and close-form analytical models cannot always provide consistently accurate results for all modes of operation of today's small devices. This has meant that there has been a greater demand for models capable of increasing our understanding of how these devices operate and capable of predicting accurate quantitative results.To simulate a device, we solve a transport equation coupled with Poisson equation The accuracy of a simulation is usually determined by how accurately carrier transport is described. Generally, the more sophisticated the approach, the heavier the computational burden, so it is important to choose an adequate approach for the device under study. In the past, the study of electric behavior in a semiconductor device has been based on the drift-diffusion equation. The drift-diffusion model is a low-order approximation of the Boltzmann transport equation, it implies that mobility of the carrier is only a function of the local electrical field and it does not take account of the non-stationary characteristics such as carrier heating and velocity overshoot [1,2]. The application of this model is limited to devices where the spatial variation of the electric field is not very large. However, in modern devices, whose size is in the deep submicron region, the nonstationary phenomena are becoming more important. As a result, the drift-diffusion model is no longer applicable [3][4][5][6].Monte Carlo simulation has been widely used for analyzing carrier transport in bulk semiconductors [7,8,9]. This method tracks the momentum and position of an ensemble of carriers as they move through a device under the influence of an electric field and random scattering forces. Random numbers are chosen to determine the time between collisions, the type of scattering ev...

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Two-dimensional simulation of the drain-current transient effect in GaAs MESFETs

Lee

1991

Solid-State Electronics

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Half-implicit difference scheme for numerical simulation of transient processes in semiconductor devices

Cited by 15 publications

References 13 publications

Polarization kinetics in ferroelectrics with regard to fluctuations

Polarization kinetics in ferroelectrics with regard to fluctuations

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Two-dimensional simulation of the drain-current transient effect in GaAs MESFETs

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